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{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "L:=9/2+I*sqrt(7)/2:   B:=evalm(A-L)
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6#-%'matrixG6#7%7%\"\"\"\"\"!,$**\"\"%F(,&F(!\"\"*&\"\"(#F(\"\"#^#F(F(
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "for i to 3 do for j to 3 do \+
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{XPPMATH 20 "6#,&#\"\"\"\"\"#!\"\"*&^##F%F&F%\"\"(F*F%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "q:=[2,1-I*sqrt(7),2];" }}{PARA 11 "
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{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%,&\"\"*\"\"\"*&\"\"(#F)
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{MPLTEXT 1 0 21 "simplify(evalm(q*L));" }}{PARA 11 "" 1 "" {XPPMATH 
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "restart:A:=matrix(4,4,[2,-1,
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"6#>%\"AG-%'matrixG6#7&7&\"\"#!\"\"\"\"\"F+7&\"\"$\"\"'!\"$F.7&\"\"&F2
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}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7&7&,&\"\"#\"\"\"%
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r j from i+1 to 4 do B:=simplify(addrow(B,i,j,-B[j,i]/B[i,i]));print(B
) end do end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&,&
\"\"#\"\"\"%\"LG!\"\"F,F*F,7&\"\"!,$*&,(\"#:F**&\"\")F*F+F*F,*$)F+F)F*
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FGF:,$F+F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&,&\"\"#
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,&\"\"#\"\"\"%\"LG!\"\"F,F*F,7&\"\"!,$*&,(\"#:F**&\"\")F*F+F*F,*$)F+F)
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.F.,$*(F+F*F;F*,&F+F*\"\"&F,F,F,,$*(FBF*F;F*FAF,F*7&F.F.,$*(F:F*F;F*FA
F,F*,$*&,(\"\"'F**&FBF*F+F*F,F5F*F*FAF,F," }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7&7&,&\"\"#\"\"\"%\"LG!\"\"F,F*F,7&\"\"!,$*
&,(\"#:F**&\"\")F*F+F*F,*$)F+F)F*F*F*,&F)F,F+F*F,F,,$*(\"\"$F*,&F:F,F+
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0 "" {MPLTEXT 1 0 22 "quo(L^2-8*L+15,L-5,L);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&\"\"$!\"\"%\"LG\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 39 "3 is a triple root, -3 is a simple one." }{MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gausselim(A-L);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"$,&\"\"'\"\"\"%\"L
G!\"\"!\"$F(7&\"\"!,&F(F+F,F-F0F17&F0F0F1,&\"\"&F+*(F4F+F(F-F,F+F-7&F0
F0F0,&F(F-*&F(F-F,\"\"#F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"\"\"!F)#!\"\"\"
\"$7&F)F(F)F(7&F)F)F(#\"\"&F,7&F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "q:=[1,-3,-5,3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"qG7&\"\"\"!\"$!\"&\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "evalm(A&*q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&!\"$
\"\"*\"#:!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(
A-3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"F(!\"\"
F(7&\"\"!F+F+F+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "q1:=
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0 "" {MPLTEXT 1 0 13 "evalm(A&*q1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%'vectorG6#7&!\"$\"\"$\"\"!F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "evalm(A&*q2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7
&\"\"$\"\"!F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalm(A&
*q3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&!\"$\"\"!F(\"\"
$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "
restart:A:=matrix(4,4,[5,1,2,-1,-4,2,-2,-26,-3,-2,-1,11,-6,-3,-6,-3]);
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"&\"\"
\"\"\"#!\"\"7&!\"%F,!\"#!#E7&!\"$F0F-\"#67&!\"'F3F6F3" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" 
{TEXT -1 80 "Warning, the protected names norm and trace have been red
efined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 
"gausselim(A-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&!
\"%,&\"\"#\"\"\"%\"LG!\"\"!\"#!#E7&\"\"!,&\"\"'F-*(\"\"$F+F*F-F,F+F+!
\"$,&\"#OF+F,F-7&F1F1*&,(\"\"*F+*&F3F+F,F+F-*$)F,F*F+F+F+,&\"\"%F-F,F+
F-,$*(F3F-,*\"$+$F+*&\"#\"*F+F,F+F-*&FAF+F?F+F-*$)F,F5F+F+F+F@F-F+7&F1
F1F1,(*&#F+F3F+F>F+F+*&#F+F*F+F,F+F+F5F-" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 39 "3 is a triple root, -6 is a simple one." }{MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+6);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"\"\"!F)F)7&F)F(F
)!\"$7&F)F)F(F(7&F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "q:=[0,3,-1,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG7&\"\"!\"
\"$!\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A&*
q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!!#=\"\"'!\"'
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A-3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"\"\"!F)F)7&F)F(
\"\"#F)7&F)F)F)F(7&F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "q:=[0,-2,1,0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG7&\"\"!!\"
#\"\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A&*q);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!!\"'\"\"$F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "B:=stackmatrix((A-3)^2,q);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7'7&\"\"!F*F*F*7&
\"$e\"\"#zF,\"$k\"7&!#_!#EF0!#b7&\"#a\"#FF4F47&F*!\"#\"\"\"F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gaussjord(%);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7&\"\"\"\"\"!#\"\"&\"\"%F)7&F)F(#!
\"\"\"\"#F)7&F)F)F)F(7&F)F)F)F)F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "s:=[-5,2,4,0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"sG7&!\"&\"\"#\"\"%\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "evalm((A-3)^2&*s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#
7&\"\"!F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "B:=stackma
trix((A-3)^3,q,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG
6#7(7&\"\"!F*F*F*7&!%e9!$H(F,F,7&\"$'[\"$V#F/F/7&!$'[!$V#F2F27&F*!\"#
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13 "gaussjord(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7(7&
\"\"\"\"\"!F)#\"\"%\"\"*7&F)F(F)#\"\"#F,7&F)F)F(F*7&F)F)F)F)F1F1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "u:=[-4,-2,-4,9]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm((A-3)^3&*u);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "restart:A:=matrix(4,4,[2,-
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20 "6#>%\"AG-%'matrixG6#7&7&\"\"#!\"$\"\"$!\"%7&\"\"\"F/F*!\"\"7&F*F-
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th(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected nam
es norm and trace have been redefined and unprotected\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gausselim(A-L);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\",&F(F(%\"LG!\"\"\"\"#F+7&\"\"!,
&\"\"'F+*&F,F(F*F(F(,&\"\"$F(F*F+F.7&F.F.,&*&F,F+F*F(F(F(F(,&F,F+F*F+7
&F.F.F.,(*$)F*F,F(F+*&F0F(F*F(F(\"\"*F+" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 25 "3 is triple, -2 is simple" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"\"\"!F)!\"\"7&F)F(F)F)7&F)F)F(F
)7&F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q:=[1,0,0,1]
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A&*q);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'vectorG6#7&!\"#\"\"!F(F'" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "gaussjord(A-3);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'matrixG6#7&7&\"\"\"\"\"!F)F(7&F)F(!\"\"F(7&F)F)F)F)F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "q1:=[0,1,1,0]:  q2:=[-1,-1,0
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{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!\"\"$F(F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalm(A&*q2);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&!\"$F'\"\"!\"\"$" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 30 "B:=stackmatrix((A-3)^2,q1,q2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7(7&\"\"!\"#D!#DF+7&F*F*F*
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{MPLTEXT 1 0 13 "gaussjord(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'m
atrixG6#7(7&\"\"\"\"\"!F)#!\"$\"\"#7&F)F(F)#F(F,7&F)F)F(#!\"\"F,7&F)F)
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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm((A-3)^2&*s);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
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